264 research outputs found
Universality class of the pair contact process with diffusion
The pair contact process with diffusion (PCPD) is studied with a standard
Monte Carlo approach and with simulations at fixed densities. A standard
analysis of the simulation results, based on the particle densities or on the
pair densities, yields inconsistent estimates for the critical exponents.
However, if a well-chosen linear combination of the particle and pair densities
is used, leading corrections can be suppressed, and consistent estimates for
the independent critical exponents delta=0.16(2), beta=0.28(2) and z=1.58 are
obtained. Since these estimates are also consistent with their values in
directed percolation (DP), we conclude that PCPD falls in the same universality
class as DP.Comment: 8 pages, 8 figures, accepted by Phys. Rev. E (not yet published
Crossovers from parity conserving to directed percolation universality
The crossover behavior of various models exhibiting phase transition to
absorbing phase with parity conserving class has been investigated by numerical
simulations and cluster mean-field method. In case of models exhibiting Z_2
symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular
automaton) the introduction of an external symmetry breaking field causes a
crossover to kink parity conserving models characterized by dynamical scaling
of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2).
In case an even offspringed branching and annihilating random walk model (dual
to NEKIMCA) the introduction of spontaneous particle decay destroys the parity
conservation and results in a crossover to the DP class characterized by the
crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover
operators can't be mapped onto each other and the resulting models show a
diversity within the DP universality class in one dimension. These
'sub-classes' differ in cluster scaling exponents.Comment: 6 pages, 6 figures, accepted version in PR
Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model
We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile
automata as a closed system with fixed energy.
We explore the full range of energies characterizing the active phase. The
model exhibits strong non-ergodic features by settling into limit-cycles whose
period depends on the energy and initial conditions. The asymptotic activity
(topplings density) shows, as a function of energy density , a
devil's staircase behaviour defining a symmetric energy interval-set over which
also the period lengths remain constant. The properties of -
phase diagram can be traced back to the basic symmetries underlying the model's
dynamics.Comment: EPL-style, 7 pages, 3 eps figures, revised versio
Absorbing-state phase transitions: exact solutions of small systems
I derive precise results for absorbing-state phase transitions using exact
(numerically determined) quasistationary probability distributions for small
systems. Analysis of the contact process on rings of 23 or fewer sites yields
critical properties (control parameter, order-parameter ratios, and critical
exponents z and beta/nu_perp) with an accuracy of better than 0.1%; for the
exponent nu_perp the accuracy is about 0.5%. Good results are also obtained for
the pair contact process
A supercritical series analysis for the generalized contact process with diffusion
We study a model that generalizes the CP with diffusion. An additional
transition is included in the model so that at a particular point of its phase
diagram a crossover from the directed percolation to the compact directed
percolation class will happen. We are particularly interested in the effect of
diffusion on the properties of the crossover between the universality classes.
To address this point, we develop a supercritical series expansion for the
ultimate survival probability and analyse this series using d-log Pad\'e and
partial differential approximants. We also obtain approximate solutions in the
one- and two-site dynamical mean-field approximations. We find evidences that,
at variance to what happens in mean-field approximations, the crossover
exponent remains close to even for quite high diffusion rates, and
therefore the critical line in the neighborhood of the multicritical point
apparently does not reproduce the mean-field result (which leads to )
as the diffusion rate grows without bound
Response of a catalytic reaction to periodic variation of the CO pressure: Increased CO_2 production and dynamic phase transition
We present a kinetic Monte Carlo study of the dynamical response of a
Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic
variation of the CO presure. We use a square-wave periodic pressure variation
with parameters that can be tuned to enhance the catalytic activity. We produce
evidence that, below a critical value of the desorption rate, the driven system
undergoes a dynamic phase transition between a CO_2 productive phase and a
nonproductive one at a critical value of the period of the pressure
oscillation. At the dynamic phase transition the period-averged CO_2 production
rate is significantly increased and can be used as a dynamic order parameter.
We perform a finite-size scaling analysis that indicates the existence of
power-law singularities for the order parameter and its fluctuations, yielding
estimated critical exponent ratios and . These exponent ratios, together with theoretical symmetry
arguments and numerical data for the fourth-order cumulant associated with the
transition, give reasonable support for the hypothesis that the observed
nonequilibrium dynamic phase transition is in the same universality class as
the two-dimensional equilibrium Ising model.Comment: 18 pages, 10 figures, accepted in Physical Review
Series expansion for a stochastic sandpile
Using operator algebra, we extend the series for the activity density in a
one-dimensional stochastic sandpile with fixed particle density p, the first
terms of which were obtained via perturbation theory [R. Dickman and R.
Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time;
the coefficients are polynomials in p. We devise an algorithm for evaluating
expectations of operator products and extend the series to O(t^{16}).
Constructing Pade approximants to a suitably transformed series, we obtain
predictions for the activity that compare well against simulations, in the
supercritical regime.Comment: Extended series and improved analysi
Spinodal Decomposition and the Tomita Sum Rule
The scaling properties of a phase-ordering system with a conserved order
parameter are studied. The theory developed leads to scaling functions
satisfying certain general properties including the Tomita sum rule. The theory
also gives good agreement with numerical results for the order parameter
scaling function in three dimensions. The values of the associated
nonequilibrium decay exponents are given by the known lower bounds.Comment: 15 pages, 6 figure
Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process
We consider the dynamics of the disordered, one-dimensional, symmetric zero
range process in which a particle from an occupied site hops to its nearest
neighbour with a quenched rate . These rates are chosen randomly from the
probability distribution , where is the lower cutoff.
For , this model is known to exhibit a phase transition in the steady
state from a low density phase with a finite number of particles at each site
to a high density aggregate phase in which the site with the lowest hopping
rate supports an infinite number of particles. In the latter case, it is
interesting to ask how the system locates the site with globally minimum rate.
We use an argument based on local equilibrium, supported by Monte Carlo
simulations, to describe the approach to the steady state. We find that at
large enough time, the mass transport in the regions with a smooth density
profile is described by a diffusion equation with site-dependent rates, while
the isolated points where the mass distribution is singular act as the
boundaries of these regions. Our argument implies that the relaxation time
scales with the system size as with for and
suggests a different behaviour for .Comment: Revtex, 7 pages including 3 figures. Submitted to Pramana -- special
issue on mesoscopic and disordered system
Continuously-variable survival exponent for random walks with movable partial reflectors
We study a one-dimensional lattice random walk with an absorbing boundary at
the origin and a movable partial reflector. On encountering the reflector, at
site x, the walker is reflected (with probability r) to x-1 and the reflector
is simultaneously pushed to x+1. Iteration of the transition matrix, and
asymptotic analysis of the probability generating function show that the
critical exponent delta governing the survival probability varies continuously
between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism
for nonuniversal kinetic critical behavior, observed in models with an infinite
number of absorbing configurations.Comment: 5 pages, 3 figure
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